Problems in Plane Stress

Abstract

In many problems of practical interest, it is a reasonable approximation to disregard the elastic component of strain in the theoretical analysis even when the body is only partially plastic. In effect, we are then dealing with a hypothetical material which is rigid when stressed below the elastic limit, the modulus of elasticity being considered as infinitely large. If the plastically stressed material has the freedom to flow in some direction, the distribution of stress in the deforming zone of the assumed rigid/plastic body would approximate that in an elastic/plastic body, except in a transition region near the elastic/plastic interface where the deformation is restricted to elastic order of magnitude. The assumption of rigid/plastic material is generally adequate not only for the analysis of technological forming processes, where the plastic part of the strain dominates over the elastic part, but also for the estimation of the yield point load when the rate of work-hardening is sufficiently small (Section 1.2). In the present chapter, we shall be concerned with problems in plane stress involving rigid/plastic bodies which are loaded beyond the range of contained plastic deformation.